# Re: [Wien] f orbital under an external magnetic field

```Dear Bin Shao,

```
unfortunately I am travelling and won't be able to contribute during the next days. I am looking forward to comments from people with experience in calculations with rare earths.
```
```
May I just ask why you go for the energy and not for the magnetization or the susceptibility? If there is some change of the crystal field ground state this should show. From your calculation you get the size of the magnetic moments for a given field, from that you get a susceptibility. From what you say something happens around 4 T. I cannot guess from the information I have what, but I would expect it to show in the susceptibility as well.
```
Good luck with this interesting problem

Martin Pieper

---
Dr. Martin Pieper
Karl-Franzens University
Institute of Physics
Universitätsplatz 5
A-8010 Graz
Austria
Tel.: +43-(0)316-380-8564

Am 06.08.2015 15:47, schrieb Bin Shao:
```
```Dear Martin Pieper，

Actually, I intend to demonstrate that the energy difference between
the ground state of Er^3+ (S=3/2; L=6; J=15/2) and the excited state
(S=3/2; L=0; J=3/2) can be tuned by the external magnetic field, With
the magnetic filed and the crystal field, the excited state splits
into four states, |+3/2>, |+1/2>, |-1/2>, and |-3/2>. For the 45 Tesla
magnetic field, the delta energy between the |+3/2> and |-3/2> is over
10 meV. Since we can not directly get the excited state in wien2k,
even by forcing the occupation number, the calculation will still be
trick.

However, because the spin quantum number of the two states is the same
(S=3/2), there is no spin flip from the ground state to the excited
state. In this case, we can estimate the energy difference between the
ground state and the excited state by calculating the energy
difference between the occupied states of f electron in minority spin
of the ground state and the unoccupied counterparts in minority spin
of the ground state. The energy difference should become smaller with
increasing the magnetic field, which can be attributed to the lower in
energy of the |-3/2> state relative to the |+/-3/2> state with no
magnetic field.

Since the energy shift is in the magnitude of meV, we can not seen
this shift from the dos calculation due to the smear of the dos. Since
the f band is usually very local and the band is very flat, so I
checked the eigenvalues of the 7 f-electron at the Gamma point and try
to show the energy shift from the variations of the eigenvalues.
However, the results show that there is only an energy shift from the
0 T to 4 T. When the magnetic filed is increasing, the eigenvalues are
almost the same as that of 4 T.

```
```This most probably is the old problem of the energy zero in
disguise.
```
```
This may be the problem. But I have calculated all the energy
differences between the 3 unoccupied and 4 occupied states of f
electron in minority spin, the 12 (3*4) values are keep the same trend
while the magnetic filed is varied and they are all flat. For the
different f states, they get different J and the energy shifts
(g_J*mu_B*J*B) induced by the magnetic filed should be also different.
So I am confused. It should be noted that the energy difference is
independent to the energy zero.

Best,

Bin

On Thu, Aug 6, 2015 at 7:23 PM, pieper <pie...@ifp.tuwien.ac.at>
wrote:

```
```As an afterthought:

This most probably is the old problem of the energy zero in
disguise. The Zeeman interaction you estimated and as accounted for
in Wien2k is basically g*mu_B*S*B. It gives you the energy
difference between a moment pointing up and one pointing down.
However, it has a vanishing trace, the zero is at B=0 and the center
stays there.

Best regards,

Martin Pieper

---
Dr. Martin Pieper
Karl-Franzens University
Institute of Physics
Universitätsplatz 5
A-8010 Graz
Austria
Tel.: +43-(0)316-380-8564 [3]

Am 06.08.2015 04:55, schrieb Bin Shao:

```
```Dear all,

I made calculations of a compound with Er^3+(4f^11 5d^0 6s^0,
ground
state S=3/2, L=6, J=15/2) doping under an external magnetic
field. I
got the corresponding occupation of Er^3+ with 7 electrons in
majority
spin and 4 electrons in minority spin. With soc including, I got
eigenvalues at Gamma point of the Er^3+ under the magnetic field
from
4 Tesla to 45 Tesla. However, the picture indicates that the
eigenvalues with the different magnetic fields almost keep the
same as
that of 4 T. Why? According to a simple estimation, the magnetic
field
of 45 T will introduce an energy shift about 10 meV, that would
definitely be seen from the figure.

Best regards,

Bin

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--

Bin Shao
Postdoc
Department of Physics, Tsinghua University
Beijing 100084, P. R. China
Email: binshao1...@gmail.com

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